Answer:
19.72 ft
Step-by-step explanation:
You know the tangent of an angle is the ratio of the opposite side to the adjacent side of the right triangle. So, the angle α to the bottom of the statue is ...
tan(α) = (42 ft)/(73 ft)
α = arctan(42/73) ≈ 29.914°
Then the angle to the top of the statue is ...
β = 10.3° +29.914° = 40.214°
The same tangent relationship tells us the height to the top of the statue from the base of the hill is ...
tan(β) = (height to top)/(73 ft)
Multiplying by 73 ft gives ...
height to top of statue = (73 ft)·tan(40.214°) = 61.72 ft
So, the height of the statue is the difference between the heights of its top and its base:
statue height = 61.72 ft - 42 ft
statue height = 19.72 ft
